A construction of conformal-harmonic maps

Abstract

Conformal harmonic maps from a 4-dimensional conformal manifold to a Riemannian manifold are maps satisfying a certain conformally. invariant fourth order equation. We prove a general existence result for conformal harmonic maps, analogous to the Eells-Sampson theorem for harmonic maps. The proof uses a geometric flow and relies on results of Gursky-Viaclovsky and Lamm. (c) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.